{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T23:31:04Z","timestamp":1768347064700,"version":"3.49.0"},"reference-count":34,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,3,18]],"date-time":"2020-03-18T00:00:00Z","timestamp":1584489600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Numerical simulations are performed to examine the effect of size of control rods (d1) and spacing ratio (g) on flow around a square rod with upstream and downstream control rods aligned in-line using the lattice Boltzmann method (LBM). The Reynolds number (Re) is fixed at Re = 160, while the spacing between the main rod and control rods is taken in the range 1 \u2264 g \u2264 5 and the size of the control rod is varied between 4 and 20. Seven different types of flow mods are observed in this study at different values of g and d1. Variation in force statistics, like mean drag coefficient (Cdmean), Strouhal number (St), root mean square values of drag (Cdrms) and lift coefficients (Clrms), and percentage reduction in mean drag coefficient is discussed in detail. It was examined that vortex shedding completely suppressed at (g, d1) = (1, 12), (2, 12), and (2, 16) where steady flow mode exists. Moreover, it was found that at large gap spacing, where g = 5, the effect of control rods on the main rod vanishes. Due to this strong vortex shedding produced and as a result, maximum value of Cdmean is found at (g, d1) = (5, 8). The negative values of mean drag force are also observed at some gap spacing and size of control rods are due to the effect of thrust. Furthermore, the maximum percentage reduction in Cdmean is 121%, found at (g, d1) = (2, 20).<\/jats:p>","DOI":"10.3390\/sym12030475","type":"journal-article","created":{"date-parts":[[2020,3,20]],"date-time":"2020-03-20T07:29:07Z","timestamp":1584689347000},"page":"475","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Numerical Simulation of Drag Reduction on a Square Rod Detached with Two Control Rods at Various Gap Spacing via Lattice Boltzmann Method"],"prefix":"10.3390","volume":"12","author":[{"given":"Raheela","family":"Manzoor","sequence":"first","affiliation":[{"name":"Mathematics Department, SBK Women\u2019s University, Quetta 87300, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Asma","family":"Khalid","sequence":"additional","affiliation":[{"name":"Mathematics Department, SBK Women\u2019s University, Quetta 87300, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2056-9371","authenticated-orcid":false,"given":"Ilyas","family":"Khan","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"family":"Shams-Ul-Islam","sequence":"additional","affiliation":[{"name":"Mathematics Department, COMSATS University, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Cankaya University, 06790 Ankara, Turkey"},{"name":"Institute of Space Sciences, 077125 Magurele, Romania"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5769-4320","authenticated-orcid":false,"given":"Kottakkaran Sooppy","family":"Nisar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University, Al-Kharj 16278, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1002\/1097-0363(20010228)35:4<421::AID-FLD100>3.0.CO;2-M","article-title":"Control of vortex shedding behind circular rod for flows at low Reynolds numbers","volume":"35","author":"Mittal","year":"2001","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.apor.2004.10.002","article-title":"Numerical simulation of viscous flow past two circular rods of different diameters","volume":"27","author":"Zhao","year":"2005","journal-title":"Appl. Ocean Res."},{"key":"ref_3","first-page":"514","article-title":"Numerical simulation of passive control on vortex shedding behind square rod using splitter plate","volume":"2","author":"Turki","year":"2008","journal-title":"Eng. Appl. Comput. Fluid Mech."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1016\/j.jfluidstructs.2009.05.007","article-title":"Passive control of wake on by two small control rods at Reynolds number","volume":"25","author":"Kuo","year":"2009","journal-title":"J. Fluids Struct."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.ijheatfluidflow.2011.12.008","article-title":"Reduction of fluid forces and heat transfer on a square rod in a laminar flow regime using a control plate","volume":"34","author":"Malekzadeh","year":"2012","journal-title":"Int. J. Heat Fluid Flow"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.ijheatfluidflow.2012.03.011","article-title":"Low Reynolds number flow over a square rod with a detached flat plate","volume":"36","author":"Ali","year":"2012","journal-title":"Int. J. Heat Fluid Flow"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.jfluidstructs.2012.02.004","article-title":"Experimental investigation on the suppression of vortex-induced vibration of long flexible riser by multiple control rods","volume":"30","author":"Wu","year":"2012","journal-title":"J. Fluids Struct."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.jfluidstructs.2012.11.002","article-title":"The passive control of wake flow behind a circular rod by parallel dual plates","volume":"37","author":"Bao","year":"2013","journal-title":"J. Fluids Struct."},{"key":"ref_9","unstructured":"Gupta, A. (2013). Suppression of Vortex Shedding in Flow around Square Rod Using Control Rod, Department of Mechanical Engineering, Indian Institute of Technology."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4969","DOI":"10.1007\/s12206-014-1118-y","article-title":"Suppression of fluid force on flow past a square rod with a detached flat plate at low Reynolds number for various spacing ratios","volume":"28","author":"Islam","year":"2014","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.jfluidstructs.2014.03.006","article-title":"Numerical investigation of fluid flow past circular rod with multiple control rods at low Reynolds number","volume":"48","author":"Lu","year":"2014","journal-title":"J. Fluids Struct."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1504\/PCFD.2014.064554","article-title":"Effect of arrangement of inline control plate on flow past square rod","volume":"14","author":"Vamsee","year":"2014","journal-title":"Prog. Comput. Fluid Dyn."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2169","DOI":"10.1007\/s13369-015-1648-3","article-title":"Lattice Boltzmann study of wake structures and force statistics for various gap spacings between a square rod with a detached flat plate","volume":"40","author":"Islam","year":"2015","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"045119","DOI":"10.1063\/1.4982696","article-title":"A computational study of drag reduction and vortex shedding suppression of flow past a square rod in presence of small control rods","volume":"7","author":"Islam","year":"2017","journal-title":"AIP Adv."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1007\/s13369-016-2302-4","article-title":"Effect of Reynolds number on flow past a square rod in presence of multiple control rods at various gap spacings","volume":"42","author":"Islam","year":"2017","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2023","DOI":"10.1007\/s12205-017-0239-0","article-title":"Drag reduction on a square rod using multiple detached control rods","volume":"22","author":"Islam","year":"2017","journal-title":"KSCE J. Civ. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1146\/annurev.fluid.30.1.329","article-title":"Lattice Boltzmann method for fluid flows","volume":"30","author":"Chen","year":"1998","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_18","unstructured":"Wolf-Gladrow, D.A. (2005). Lattice-Gas Cellular Automata and Lattice Boltzmann Models-An introduction, Springer."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Sukop, M.C., and Thorne, D.T. (2006). Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers, Springer.","DOI":"10.1007\/978-3-540-27982-2"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Mohammad, A.A. (2011). Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes, Springer.","DOI":"10.1007\/978-0-85729-455-5"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4955","DOI":"10.1016\/j.jcp.2008.01.024","article-title":"A comparative study of the LBE and GKS methods for 2D near incompressible laminar flows","volume":"227","author":"Guo","year":"2008","journal-title":"J. Comput. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.jfluidstructs.2006.08.011","article-title":"Numerical simulation of flow around a square rod in uniform-shear flow","volume":"23","author":"Cheng","year":"2007","journal-title":"J. Fluids Struct."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1017\/S0022112082003115","article-title":"Strouhal of rectangular rods","volume":"123","author":"Okajima","year":"1982","journal-title":"J. Fluid Mech."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/0167-6105(93)90014-F","article-title":"Flow around rectangular cylinders: Pressure forces and wake frequencies","volume":"49","author":"Norberg","year":"1993","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_25","unstructured":"Sohankar, A., Davidson, L., and Norberg, C. (1995, January 10\u201315). Numerical simulation of unsteady flow around a square two-dimensional rod. Proceedings of the Twelfth Australasian Fluid Mechanics Conference, Sydney, Australia."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1063\/1.869930","article-title":"Three-dimensional floquet instability of the wake of a square rod","volume":"11","author":"Robichuax","year":"1999","journal-title":"Phys. Fluids"},{"key":"ref_27","unstructured":"Abograis, A.S., and Alshayji, A.E. (2013, January 9\u201311). Reduction of Fluid Forces on a square rod in a laminar flow using passive control methods. Proceedings of the COMSOL Conference in Boston, Boston, MA, USA."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/0167-6105(81)90036-2","article-title":"Review and classification of various aerodynamic and hydrodynamic means for suppressing vortex shedding","volume":"7","author":"Zdravkovich","year":"1981","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2397","DOI":"10.1299\/jsme1958.27.2397","article-title":"Characteristics of the flow around three circular rods arranged inline","volume":"27","author":"Igarashi","year":"1984","journal-title":"Bull. JSME"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1017\/jfm.2012.359","article-title":"Flow around six in-line square rods","volume":"710","author":"Sewatkar","year":"2012","journal-title":"J. Fluid Mech."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1115\/1.3448871","article-title":"Review of flow interference between two circular rods in various arrangements","volume":"99","author":"Zdravkovich","year":"1977","journal-title":"J. Fluids Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1007\/s40430-014-0282-4","article-title":"Numerical investigation of wake modes for flow past three tandem rods using the multi-relaxation-time lattice Boltzmann method for different gap spacings","volume":"36","author":"Islam","year":"2016","journal-title":"J. Braz. Soc. Mech. Sci. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.ijheatfluidflow.2010.01.007","article-title":"Numerical investigation of low Reynolds number flow past two and three circular rods using unstructured grid CFR scheme","volume":"31","author":"Harichandan","year":"2010","journal-title":"Int. J. Heat Fluid Flow"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"025221","DOI":"10.1063\/1.5004631","article-title":"Numerical investigation of fluid-solid interaction for flow around three square rods","volume":"8","author":"Abbasi","year":"2018","journal-title":"AIP Adv."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/3\/475\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:07:37Z","timestamp":1760173657000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/3\/475"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,18]]},"references-count":34,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["sym12030475"],"URL":"https:\/\/doi.org\/10.3390\/sym12030475","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,18]]}}}